Internal problem ID [4675]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }-\sec \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 98
dsolve(diff(y(x),x$3)+diff(y(x),x)=sec(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right )-\cos \left (x \right ) x +\sin \left (x \right ) c_{1} -\cos \left (x \right ) c_{2} +\frac {i \left (2 i \ln \left (2\right ) \sin \left (x \right )+{\mathrm e}^{i x} \ln \left (\frac {{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )+{\mathrm e}^{i x}-4 \arctan \left ({\mathrm e}^{i x}\right )-{\mathrm e}^{-i x} \ln \left (\frac {{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )-{\mathrm e}^{-i x}\right )}{2}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 57
DSolve[y'''[x]+y'[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -(x+c_2) \cos (x)-\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+\sin (x) (\log (\cos (x))+c_1)+c_3 \\ \end{align*}